MECHANICS Problem Set 6, distributed 4/18/2012, due 5/2/2012
1. (Jos & Saletan, Chap 5, no 1) Consider a particle with mass 1, acted upon by a
e
uniform gravitational force eld (with potential 1/r), which is constrained to stay
on the surface of a sphere
MECHANICS Problem Set 5, distributed 3/28/2012, due 4/18/2012
1. (Arnold, page 20) Consider a 1D particle with unit mass moving in a potential U (x),
in other words the ODE x = U (x), whose Hamiltonian is H = T + U with T = 1 x2 .
2
Suppose the level set
MECHANICS Problem Set 4, assigned 3/7/12, due 3/28/12
These problems are concerned with linear elasticity. Problem 1 asks you to explain why an
isotropic Hookes law is described by just two constants. Problems 2 and 3 explore Korns
inequality. Problem 4 g
MECHANICS Problem Set 3, distributed 2/22/12, due 3/7/12
These problems provide practice with basic concepts of 3D nonlinear elasticity, and explore various
reductions including (i) incompressible uid dynamics, (ii) elastic membranes, and (iii) balloons.
MECHANICS Problem Set 2, distributed 2/8/12, due 2/22/2012
(1) The bending stiness of xerox paper. Recall our discussion of the xerox paper
problem from Lecture 2: consider a standard 8.5 11 sheet of paper, held at one
edge so the tangent there is vertica
MECHANICS Problem Set 1, distributed 1/25/2012, due 2/8/2012
These problems involve elastic strings. Their goal is to develop intuition about stress and
strain in this most elementary setting. You may nd it helpful to look at Chapter 3 of
Antman, which di